Observer design for apex height and vertical velocity of a single-leg hopping robot during stance phase

This article proposes an observer design for two important variables in the studies of single-leg hopping robot (SLHR), the apex height, and the vertical velocity of SLHR during its stance phase. At first, the Euler–Lagrange (EL) dynamics of SLHR are obtained and apex height is identified in the state-space representation of the EL dynamics. Apex height is the state variable that represents the robot body’s height at the top point, which keeps on changing as the robot functions. Vertical velocity is the velocity of the robot in the vertical direction. An observer design is presented in this article which will estimate these variables when required. The quality of the estimation is validated by the simulation results where the estimation error is zero which means the model output is correct and observer performance is good.

Energy Dissipation during Surface Interaction of an Underactuated Robot for Planetary Exploration

The article summarizes research on essential contributors to energy dissipation in an actuator for an exemplary planetary exploration hopping robot. It was demonstrated that contact dynamics could vary significantly depending on the surface type. As a result, regolith is a significant uncertainty factor to the control loop and plays a significant contribution in the control system development of future planetary exploration robots. The actual prototype of the actuating mechanism was tested on a reference surface and then compared with various surfaces (i.e., Syar, quartz sand, expanded clay, and quartz aggregate) to estimate the dissipation of the energy in the initial phase of hopping. Test outcomes are compared with multibody analysis. The research enhances trajectory planning and adaptive control of future hopping robots by determining three significant types of energy losses in the system and, most importantly, determining energy dissipation coefficients in contact with the various surfaces (i.e., from 4% to 53% depending on the surface type). The actual step-by-step methodology is proposed to analyze energy dissipation aspects for a limited number of runs, as it is a case for space systems.

Using Energy Shaping and Regulation for Limit Cycle Stabilization, Generation, and Transition in Simple Locomotive Systems

This paper explores new ways to use energy shaping and regulation methods in walking systems to generate new passive-like gaits and dynamically transition between them. We recapitulate a control framework for Lagrangian hybrid systems, and show that regulating a state varying energy function is equivalent to applying energy shaping and regulating the system to a constant energy value. We then consider a simple 1-dimensional hopping robot and show how energy shaping and regulation control can be used to generate and transition between nearly globally stable hopping limit cycles. The principles from this example are then applied on two canonical walking models, the spring loaded inverted pendulum (SLIP) and compass gait biped, to generate and transition between locomotive gaits. These examples show that piecewise jumps in control parameters can be used to achieve stable changes in desired gait characteristics dynamically/online.

Models of a hybrid wheeled hopping self-balanced robot

Combining wheeled structure with hopping mechanism, this paper purposes a self-balanced hopping robot with hybrid motion pattern. The main actuator which is the cylindrical cam, optimized by particle swarm optimization (PSO), is equipped with the motor to control the hopping motion. Robotic system dynamics model is established and solved by Lagrangian method. After linearization, control characteristics of the system is obtained by classical control theory based on dynamics equations. By applying Adams and Matlab to simulate the system, hopping locomotion and self-balanced capability are validated respectively, and result shows that jump height can reach 750 mm theoretically. Then PID control scheme is developed and specific models of hardware and software are settled down accordingly. Finally, prototype is implemented and series of hopping experiments are conducted, showing that with different projectile angle, prototype can jump 550 mm in height and 460 mm in length, transcending majority of other existing hopping robots.

Dynamic Modeling and Control of a Novel One-Legged Hopping Robot

SUMMARY In this article, a novel mechanism for planar one-legged hopping robots is proposed. The robot consists of a flat foot which is pinned to the leg and a reciprocating mass which is connected to the leg via a prismatic joint. The proposed mechanism performs the hopping by transferring linear momentum between the reciprocating mass and its main body. The nonlinear equations of the motion of the robot are derived using the Euler–Lagrange equations. To accomplish a stable jump, appropriate trajectories have been planned. To guarantee a stable response for this nonlinear system, a sliding-mode controller is implemented. The performance of the hopping robot is investigated through numerical simulations. The results confirm the stability of the hopping robot through the jump cycle on a flat surface and in climbing up and down ramp and stairs.